204 REFLECTION AND TRANSMISSION OF RADIO WAVES 



and B alone when ^ = by £a and Eb, and their phase difference by </>, 

 the total RF voltage received by the upper lobe is 



Eu = Ea{\ + gd) + Eb{\ - ge)e^'^ (4-49) 



and by the lower lobe 



El = Ea{\ - ge) + Eb{\ + ge)e^\ (4-50) 



The difference channel voltage is then 



En = k{\Eu\' - \El\') (4-51) 



= AkgdiE/ - En"-) 

 where k = amplifier gain, and the sum channel voltage is 

 Es = k{\EuV + \ElV) 



= 2k[{EA' + Eb' + IEaEb cos 4>) + {gey{EA'' + En' - lE^En cos «^)] 

 = 2^(£x- + Ej? + 2£A£yj cos 0). (4-52) 



The error voltage is 



Eu __ ^ Ea' — Eb~ ,. rn■^ 



Es ~ ^ Ea' + Eb' + IEaEs cos 0' ^'^"'^^ 



In the presence of only a single target, say at A, the error voltage would be 



d. (4-54) 



(t)' 



(4-56) 



Comparing this with Equation 4-53 we see that the apparent reflection 

 center of the dual-reflector target lies at an angle d' to the boresight axis 



1 - {Eb/EaY ,, ... 



1 + {Eb/EaY + 2{Eb/Ea) cos (^ ■ ^^'^'^ 



Thus, d' depends on the ratio 



^ 1 - {Eb/EaY 



' 1 + {Eb/EaY + 1{Eb/Ea) cos 4> 



and therefore on the relative amplitude and phase of the two reflections. 

 This ratio can be less than, equal to, or greater than unity in absolute value, 

 and may be positive or negative. In other words, the apparent reflection 

 center can lie anywhere within the target, or even completely outside it. 



From Equation 4-56, r = when E^a = En-, so that equal reflectors have 

 an apparent center midway between them, regardless of their relative 

 phase. For values of £«/£.! other than unity, the value of r depends on the 

 relative phase, 0. The apparent reflection center lies ovitside the target, 

 when \r\ > 1, which requires that 



Er Ei 



- cos = COS (tt -</))> 7^ or — • (4-57) 



r.,\ ■ rLB 



